∫ xarctan(x)/sqrt{1+x^2 wrt x সমাধান কৰক

$$\int{ \frac{ x \arctan ( x ) }{ \sqrt{ 1+ { x }^{ 2 } } } }d x$$

মূল্যায়ন

$$\sqrt{x^{2}+1}\arctan(x)+\ln(|\cos(\frac{\arctan(x)}{2})-\sin(\frac{\arctan(x)}{2})|)-\ln(|\sin(\frac{\arctan(x)}{2})+\cos(\frac{\arctan(x)}{2})|)+С$$

ডিফাৰেনচিয়েট w.r.t. x

$$\frac{x^{3}\arctan(x)\cos(\arctan(x))+\left(x\cos(\frac{\arctan(x)}{2})\right)^{2}-\left(x\sin(\frac{\arctan(x)}{2})\right)^{2}+x\arctan(x)\cos(\arctan(x))+\cos(\arctan(x))-\sqrt{x^{2}+1}}{\sqrt{x^{2}+1}\left(\left(x\cos(\frac{\arctan(x)}{2})\right)^{2}-\left(x\sin(\frac{\arctan(x)}{2})\right)^{2}+\cos(\arctan(x))\right)}$$